6. Graphs. (a) Consider the undirected graph G (V, E), with vertex set V (u, u2, us, us us, uo ur) and the set of edges E-: {(ur, u), (u7, ua), (u7, ua), (u7, t4), (u7,?5), (Ur, te), (ui, t12), (u2,us), (u3, u4), (u4, us), (us, ue). (u,ui)) i. (2) Draw a graphical representation of G. i. (2) Write the adjacency matrix of the graph G ii. (2) What are the total number of paths of length two between all pairs of vertices in G? iv. (2) Is the graph G isomorphic to any member of Kn, Cn W , or Qn? Justify your answer. (b) (6) Consider the family of complete graphs Kn for n 2 1. For each question below provide an answer and a clear justification. i. For what n does Kn have an Euler cycle? ii. For what n does Kn have an Euler path? ii. For what n does Kn have a Hamilton cycle? (c) (6) Consider an undirected graph H with v vertices and e edges. The maximum degree of the vertices in H is denoted D while the minimum degree is denoted d. Show clearly and rigorously that the following two statements are true whenever v>0 D22